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- W2576805101 abstract "We define numbers of the type Oj(N) = N 0 - N 1 + N 2 - … + N 2j and E j (N) = -N 0 + N 1 - N 2 + … + N 2j+1 (j = 0, 1, 2, …) and the corresponding integer sequences. We prove that these integer sequences, e.g., S0(N) = O0(N), O1(N), …, Or(N), … and SE(N) = E0(N), E1(N), …, Er(N), … correspond to the number of odd and even walks in complete graphs KN. We then prove that there is a unique family of graphs which have exactly the same sequence of odd walks between connected nodes and of even walks between pairs of nodes at distance two, respectively. These graphs are the crown graphs: G2n = K2 ⊗ Kn." @default.
- W2576805101 created "2017-01-26" @default.
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- W2576805101 date "2013-01-01" @default.
- W2576805101 modified "2023-09-26" @default.
- W2576805101 title "Integer sequences from walks in graphs" @default.
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